two. And, again just like with leaves and shells, it seems likely that among the animals we see are ones that correspond to a fair fraction of the possible choices for relative rates of growth.

We began this section by asking what underlying rules of growth would be needed to produce the kind of diversity and complexity that we see in the forms of plants and animals. And in each case that we have examined what we have found is that remarkably simple rules seem to suffice. Indeed, in most cases the basic rules actually seem to be somewhat simpler than those that operate in many non-biological systems. But what allows the striking diversity that we see in biological systems is that different organisms and different species of organisms are always based on at least slightly different rules.

In the previous section I argued that for the most part such rules will not be carefully chosen by natural selection, but instead will just be picked almost at random from among the possibilities. From experience with traditional mathematical models, however, one might then assume that this would inevitably imply that all plants and animals would have forms that look quite similar.

But what we have discovered in this book is that when one uses rules that correspond to simple programs, rather than, say, traditional mathematical equations, it is very common to find that different rules lead to quite different—and often highly complex—patterns of behavior. And it is this basic phenomenon that I suspect is responsible for most of the diversity and complexity that we see in the forms of plants and animals.

Biological Pigmentation Patterns

At a visual level, pigmentation patterns represent some of the most obvious examples of complexity in biological organisms. And in the past it has usually been assumed that to get the kind of complexity that one sees in such patterns there must be some highly complex underlying mechanism, presumably related to optimization through natural selection.

Following the discoveries in this book, however, what I strongly suspect is that in fact the vast majority of pigmentation patterns in